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Show that A(-3, 2), B(-5,-5), C(2,-3) and D(4,4) are the vertices of a rhombus.

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 Let A(-3, 2), B(-5,-5), C(2,-3) and D(4,4) are the vertices of a rhombus.

Coordinates of the midpoint of AC are

Coordinates of the midpoint of BD are 

Thus, AC and BD have the same midpoint

Hence, ABCD is a parallelogram

So, ABCD is a parallelogram whose adjacent sides are equal.

Hence, ABCD is a rhombus.

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